Free energies of molecular clusters determined by guided mechanical disassembly

Abstract

The excess free energy of a molecular cluster is a key quantity in models of the nucleation of droplets from a metastable vapour phase; it is often viewed as the free energy arising from the presence of an interface between the two phases. We show how this quantity can be extracted from simulations of the mechanical disassembly of a cluster using guide particles in molecular dynamics. We disassemble clusters ranging in size from 5 to 27 argon-like Lennard-Jones atoms, thermalised at 60 K, and obtain excess free energies, by means of the Jarzynski equality, that are consistent with previous studies. We only simulate the cluster of interest, in contrast to approaches that require a series of comparisons to be made between clusters differing in size by one molecule. We discuss the advantages and disadvantages of the scheme and how it might be applied to more complex systems.

Free energy of formation of clusters of sulphuric acid and water molecules determined by guided disassembly

“…Mechanically, these extractions were typically irreversible, which also implied a thermodynamic irreversibility, in the sense that a significant fraction of the exerted work was converted into heat and passed to the heat bath. The contrast with argon cluster separation in earlier work [23] was brought about by the stronger intermolecular interactions in the present system.…”

“…Furthermore, it is quite possible that the microscopic interactions used in this study are in need of improvement: an extended model that permits proton transfer has recently been developed and could be used to rectify some of its deficiencies [36]. A similar situation was encountered in the earlier demonstration of the cluster disassembly procedure for a single species, argon [23]. The extracted cluster thermodynamic properties were consistent with other studies that used the same Lennard-Jones interactions, but the implied correspondence with experimental nucleation rates for that substance was known to be poor [3,37].…”

“…We employ a method for cluster disassembly based upon that developed in earlier work [23]. We study clusters of sulphuric acid and water, ranging in size from dimers up to a cluster of twelve molecules.…”

“…We first carried out a simple pulling protocol in which the guide particles separate at a constant speed for the duration of the simulation. The tethers start to tighten after 20% of the total separation time and reach their maximum strength at 80%, in a fashion that was successfully employed in the disassembly of argon clusters [23]. The radius of the sphere on which all but one of the guide particles are finally distributed is 25 Å, and the ultimate value of the tether strength is 0.60 kJ mol -1 Å -2 .…”

“…The approach employs the Jarzynski equality [24], according to which the mechanical work performed on a system during a nonequilibrium process can be related to a change in equilibrium Helmholtz free energy. The method, denoted cluster disassembly, can be regarded as an MD version of thermodynamic integration [25] and it has some intuitively appealing features [23]. External forces are used to pull a cluster apart into its constituent molecules in a controlled or guided fashion.…”